Fast solution of the method for controlling the circulation of airfoils using the magnus and coanda effects

Abstract

The present application relates to a method for quickly solving the circulation of airfoils controlled by Magnus and Coanda effect, comprising: determining the circulation of the airfoil without control; studying the increased circulation of the airfoil when the rotation of the rotating body at the tail of the airfoil produces the Magnus effect, and determining it through CFD; studying the increased circulation of the airfoil when the Coanda effect is produced by blowing alone, and determining it through CFD; studying the gain circulation of the airfoil when the rotation of the rotating body at the tail of the airfoil and blowing simultaneously act, and determining it through CFD; determining the total circulation Γ according to the sum of the circulation, the increased circulation, the increased circulation and the gain circulation 总 According to the Joukowski lift formula, the predicted lift is obtained. The present method uses CFD data, combines classical potential flow theory and traditional physical principles, simplifies the relationship between variables, and can greatly improve the prediction efficiency of the controlled flow field, and has strong engineering application value.

Description

Technical Field

[0001] This invention relates to the field of aircraft technology, and in particular to a method for rapidly solving airfoil circulation using the Magnus and Coanda effects. Background Technology

[0002] Lift enhancement and drag reduction are effective means to improve the aerodynamic performance of aircraft. In recent years, lift enhancement technologies based on the Magnus Effect have gradually attracted attention. This effect refers to the lateral force experienced by a rotating object moving at a certain velocity in a flow field, causing the object's trajectory to deflect; this force is called the Magnus force. Currently, research on this effect is mostly focused on fundamental areas such as hydrodynamic hull stabilizers or flow around rotating bodies. Its advantages in ship propulsion and other fields have prompted us to consider the possibility of applying it to aircraft propulsion and wing performance improvement.

[0003] Another lift-enhancing and drag-reducing technology is the circulation control method based on the Coanda Effect. This technology enhances the circulation around the wing by altering the cross-sectional shape of the wing's trailing edge, causing the internal jet to adhere to the wall as it exits. While generating the same lift, this method effectively reduces load, saves fuel, and improves energy efficiency.

[0004] Although current research indicates that the combined application of these two control methods is highly feasible, the mechanism of this coupling effect has not yet been well explained.

[0005] Based on the classical potential flow theory in fluid mechanics, the Zhukovsky transformation can be used to transform the flow around an airfoil into a flow around a rotating body formed by the superposition of straight uniform flow, dipoles, and point vortices (as shown in the attached figure). Figure 3 As shown in the diagram, the straight uniform flow characterizes the properties of the incoming flow, the dipole characterizes the thickness of the airfoil, and the point vortex characterizes the camber of the airfoil. According to the Zhukovsky lift formula, i.e. Lift can be expressed as the incoming flow density. Incoming flow velocity and the velocity circulation around the airfoil The product of the three. However, while classical potential flow theory can quickly calculate the lift of an airfoil, it cannot explain some real-world physical phenomena, such as the viscosity of fluids and the development of the boundary layer. This is because in potential flow theory, lift is only related to the circulation of the singularity in a point vortex, while in reality, lift is the result of multiple factors.

[0006] While computational fluid dynamics (CFD) methods can calculate the flow field controlled by the Magnus and Coanda effects and provide relatively accurate and reliable results, they require a large amount of computational resources and time, which is not conducive to the application of airfoil design in engineering. Summary of the Invention

[0007] This invention provides a method for rapidly solving the circulation of airfoils controlled by the Magnus and Coanda effects. This method uses a small amount of CFD data, combined with classical potential flow theory and traditional physics principles, to simplify the relationships between some variables, which can significantly improve the prediction efficiency of the controlled flow field and has strong engineering application value.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: Methods for quickly solving airfoil circulation control using Magnus and Coanda effects include: Determine the circulation of the airfoil without control. ; The increase in circulation when the rotation of the rotating body at the airfoil tail generates the Magnus effect is studied. And determine the increase in circulation using CFD. ; The study investigates the increase in circulation of an airfoil when the Coanda effect is generated by a single blow-out airflow. And determine the increase in circulation using CFD. ; Study the gain circulation when the rotating body at the airfoil tail is rotating and air blowing is acting simultaneously. And determine the gain circulation using CFD. ; Based on the above circulation Increase circulation Increase circulation and gain circulation The sum determines the total circulation Γ 总 The predicted lift is derived based on the Zhukovsky lift formula.

[0009] Preferably, the circulation of the airfoil under uncontrolled conditions is determined. The specific process is as follows: The lift is calculated by consulting a lift coefficient table and considering the incoming flow conditions, or by obtaining the lift through CFD, and the circulation is then derived using the Zhukovsky lift formula. ; Alternatively, the circulation can be directly obtained through the Zhukovsky transform combined with the Kutta condition. .

[0010] Preferably, increase circulation volume The determination process is as follows: When the rotational speed of the rotating body at the airfoil tail is not high and gas flow does not separate, increasing circulation is beneficial. The calculation formula is as follows: ; in, These are the linear coefficients of the Magnus effect. It is the increase in circulation that occurs when the rotating body generates the Magnus effect. Let be the angular velocity of the rotating body during rotation, and Multiple sets of values ​​can be taken; Using CFD to obtain rotating bodies at different angular velocities Subtract from the following sets of circulation quantities under rotational conditions: Different angular velocities were obtained. Corresponding And through multiple sets of angular velocities and The linear fitting coefficients of the Magnus effect were obtained through a fitting algorithm. Based on the above increase in circulation The calculation formula, and based on and specific angular velocity The result is an increase in circulation. .

[0011] Preferably, increase circulation volume The determination process is as follows: When the air jet velocity is low and the air jet develops close to the rotating body without flow separation, increasing circulation is beneficial. The calculation formula is as follows: ; in, It is the jet gain coefficient under the Coanda effect. It is the increase in circulation when the blowing jet produces the Coanda effect. The velocity of the blowing jet, and Multiple sets of values ​​can be taken; Obtaining different blowing jet velocities using CFD Subtract the following sets of circulation quantities respectively Different blowing jet velocities were obtained. Corresponding And through multiple sets of air jet velocities and The fitting coefficients of the jet gain under the Coanda effect were obtained through a fitting algorithm. Based on the above increase in circulation The calculation formula, and based on and specific blowing jet velocity The result is an increase in circulation. .

[0012] Preferably, gain circulation The determination process is as follows: Gain circulation The calculation formula is as follows: ; in, It is the nonlinear coupling gain coefficient when the Magnus effect and the Coanda effect are present. This refers to the increased circulation due to the coupling gain effect in the presence of the Magnus and Coanda effects. , These are the rotational angular velocities. and the velocity of the blowing jet Weights on the contribution of the coupling gain circulation; Using CFD to obtain rotating bodies at different rotational angular velocities Air jet velocity Circulation at time Subtract respectively Subtract the corresponding , The rotating body is obtained by using different angular velocities. Air jet velocity Gain circulation at time Solve according to the fitting algorithm , , Based on the above gain circulation The calculation formula, and based on , , and specific blowing jet velocity angular velocity of the rotating body derive the gain circulation .

[0013] Preferably, the least squares method can be used to solve the problem. , , The specific solution process is as follows: Gain circumference The calculation formula is converted to And record , , And define the matrix: , , ; in, It is the flow control parameter matrix. It is the coupling gain circumductance matrix. It is a matrix of parameters to be determined; The relationship between the three matrices above is as follows: Then the undetermined parameter matrix is ​​estimated by least squares. The calculation formula is as follows: ; In this context, the superscript "-1" indicates the inverse of the correlation matrix, and the superscript "T" indicates the transpose of the correlation matrix. These are the nonlinear coupling gain fitting coefficients of the least squares fitting. , It is the fitting weight of rotational angular velocity and blowing jet velocity.

[0014] Preferably, the total circulation Γ 总 The calculation formula is as follows: .

[0015] Preferably, the formula for calculating the predicted lift is as follows: ; in, It is the incoming flow density. It is the incoming flow velocity; It is the total circulation volume; It predicts lift.

[0016] Preferably, and Obtained by least squares fitting.

[0017] Preferably, the cross-sectional shape of the rotating body can be one of a circle, an ellipse, or a triangle.

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. Using circulation to study airfoils controlled by Magnus and Coanda effects can eliminate the influence of incoming flow density and velocity, making it easier to conduct normalization studies.

[0019] 2. By using CFD to obtain a small amount of data, the circulation rate can be increased. Increase circulation and gain circulation Then the total circulation Γ is obtained. 总 Then, the predicted lift is obtained through the Zhukovsky lift formula, which combines CFD and potential flow theory. This approach avoids the need to completely calculate the flow field controlled by the Magnus and Coanda effects through CFD, which would consume a lot of computational resources and time, and also avoids the need to completely calculate the lift of the airfoil through potential flow theory, which would lead to inaccurate lift prediction. Instead, it combines CFD and potential flow theory, which simplifies the relationship between some variables and can significantly improve the prediction efficiency of the controlled flow field, thus having strong engineering application value. Attached Figure Description

[0020] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0021] Figure 1 This is a flowchart of the method for rapid calculation of airfoil circulation in an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating airfoil circulation control using the Magnus and Coanda effects in an embodiment of the present invention. Figure 3 This is a schematic diagram of the flow around a cylinder obtained by superimposing a straight uniform flow, a dipole, and a point vortex in an embodiment of the present invention. Detailed Implementation

[0022] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0024] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0025] This invention provides a method for rapidly solving the circulation of an airfoil controlled by the Magnus and Coanda effects, such as... Figure 1As shown, it specifically includes: S1: Determine the circulation of the airfoil without control. The aforementioned lack of control specifically refers to the fact that the rotating body at the trailing edge of the airfoil neither rotates nor blows air jets. S2: Investigate and determine the increase in circulation when the rotation of the rotating body at the airfoil tail produces the Magnus effect. And determine the increase in circulation using CFD. ; S3: Investigating the increase in circulation of an airfoil when the Coanda effect is generated by airflow alone. And determine the increase in circulation using CFD. ; S4: Study the gain circulation when the rotating body at the airfoil tail is rotating and air blowing is simultaneously applied. And determine the gain circulation using CFD. ; S5: Based on the above circulation... Increase circulation Increase circulation and gain circulation The sum determines the total circulation Γ 总 The predicted lift is derived based on the Zhukovsky lift formula.

[0026] The above method has the following advantages: 1. The circulation obtained in S1-S5 Increase circulation Increase circulation and gain circulation All calculations are performed using the Zhukovsky lift formula, where circulation is obtained by dividing lift by inflow density and velocity. This converts predicted lift into circulation calculation, allowing for the elimination of the influence of inflow density and velocity on circulation when studying airfoils controlled by the Magnus and Coanda effects. Finally, circulation is converted into lift, facilitating convenient, rapid, and accurate normalization studies of predicted airfoil lift. 2. Additional circulation is calculated by using CFD to obtain partial data. Increase circulation and gain circulation Then the total circulation Γ is obtained. 总 Then, the predicted lift is obtained through the Zhukovsky lift formula, which combines CFD and potential flow theory. This approach avoids the need to calculate the flow field controlled by the Magnus and Coanda effects entirely through CFD, which would consume a lot of computational resources and time, and also avoids the need to calculate the predicted airfoil lift entirely through potential flow theory, which would lead to inaccurate lift predictions. Instead, by combining CFD and potential flow theory, the relationship between some variables is simplified, which can significantly improve the prediction efficiency of the controlled flow field and has strong engineering application value.

[0027] Specifically, the first step involves determining the circulation of the airfoil without control. The process is as follows: First, determine the lift of the rotating body at the airfoil trailing edge without control. The cross-sectional shape of the rotating body can be circular, elliptical, or triangular. "Uncontrolled" specifically means that the rotating body at the airfoil trailing edge neither rotates nor blows air jets. The uncontrolled lift can be calculated by referring to a lift coefficient table and considering the incoming flow conditions, or by obtaining partial data through CFD. After obtaining the uncontrolled lift L of the rotating body at the airfoil trailing edge, calculate it using the Zhukovsky lift formula, i.e., by dividing the lift by the incoming flow density. and incoming flow velocity Obtain circulation without control Furthermore, the lift L of the rotating body at the trailing edge of the airfoil when uncontrolled can be directly obtained through the Zhukovsky transformation combined with the Kutta condition, which will not be elaborated further.

[0028] Specifically, the second step determines the increase in circulation. The process is as follows: This causes the rotating body at the trailing edge of the airfoil to rotate, and the angular velocity of the rotating body is set to... When the velocity of the blowing jet is 0, and the rotating body rotates, the Magnus effect occurs. When the rotational speed of the cylinder is not high and the gas flow does not separate from the rotating body, the increase in circulation due to the Magnus effect can be considered to be proportional to the angular velocity. Establishing a linear relationship between the additional circulation generated by the rotation of the rotating body and the rotational angular velocity facilitates rapid calculation, and the formula for calculating the increase in circulation is as follows: ; in, These are the linear coefficients of the Magnus effect. It is the increase in circulation that occurs when the rotating body generates the Magnus effect. Let be the angular velocity of the rotating body during rotation, and It can take n sets of values, with the smallest value of n being 1.

[0029] CFD can be used to obtain the rotational body at different angular velocities. The lift forces L under the given conditions were calculated using the Zhukovsky lift formula to obtain the total circulation under the Magnus effect. The circulation of the rotating body under no-control conditions was then subtracted from each of these total circulation values. Different angular velocities can be obtained. The corresponding groups of Magnus effects under the increased circulation In order to more accurately obtain the increase in circulation under the Magnus effect Through the above multiple sets of angular velocities and increase circulation The linear fitting coefficients of the Magnus effect were obtained through a fitting algorithm. Based on the above increase in circulation The calculation formula, and based on and specific angular velocity To obtain a more accurate result for increasing circulation. The calculation formula is as follows: .

[0030] Specifically, the third step determines the increase in circulation. The process is as follows: This prevents the rotating body at the trailing edge of the airfoil from rotating, allowing the blowing jet to... When the air jet is ejected at a high speed, the rotating body can produce the Coanda effect. When the air jet velocity is low and it develops close to the rotating body without flow separation, the increase in circulation due to the Coanda effect can be considered proportional to the effect of the air jet. Establishing a linear relationship between the additional circulation generated by the rotation of the body and the effect of the air jet facilitates rapid calculation, thus ensuring that the increase in circulation... The calculation formula is as follows: ; in, It is the jet gain coefficient under the Coanda effect. It is the increase in circulation when the blowing jet produces the Coanda effect. The velocity of the blowing jet, and You can take n sets of values, where the minimum value of n is 1; CFD can be used to obtain the rotating body at different blowing jet velocities. The lift L values ​​were calculated using the Zhukovsky lift formula to obtain the total circulation under the Coanda effect. The circulation of the rotating body under no-control conditions was then subtracted from each of the obtained total circulation values. Different blowing jet velocities can be obtained. The corresponding groups of increased circulation under the Coenda effect To more accurately obtain the increase in circulation under the Coanda effect Through the above-mentioned multiple sets of air jet velocities and increase circulation The fitting coefficients of the jet gain under the Coanda effect were obtained through a fitting algorithm. Based on the above increase in circulation The calculation formula, and based on and specific blowing jet velocity To obtain a more accurate result for increasing circulation. The calculation formula is as follows: .

[0031] Specifically, in the fourth step, the gain circulation... The determination process is as follows: This causes the rotating body to move at an angular velocity Rotating, and the velocity of the blowing jet is Since the gas flow around the airfoil is simultaneously affected by the rotation of the rotating body and the blowing jet, there is a nonlinear coupling gain effect of the Magnus effect and the Coanda effect, resulting in a gain circulation. ,like Figure 2 As shown, where Figure 2 In the figure, 1 represents the incoming flow condition, 2 represents the airfoil, 3 represents the circulation around the airfoil, and 4 represents the airfoil trailing edge deceleration. A rotating cylinder, labeled 5, with the airfoil trailing edge at a speed of Ejected jet; gain circulation The specific calculation formula is as follows: ; in, It is the nonlinear coupling gain coefficient when the Magnus effect and the Coanda effect are present. This refers to the increased circulation due to the coupling gain effect in the presence of the Magnus and Coanda effects. , These are the rotational angular velocities. and the velocity of the blowing jet Weights on the contribution of the coupling gain circulation; Using CFD to obtain rotating bodies at different rotational angular velocities Air jet velocity The circulation Γ at time, respectively subtract Subtract the corresponding and The rotating body is obtained by using different rotational angular velocities. Air jet velocity Gain circulation at time To obtain the gain circulation under the Magnus effect and the Coanda effect more accurately Through the above multiple sets of rotational angular velocities Air jet velocity and gain circulation The fitting coefficients of the nonlinear coupling gain under the Magnus effect and the Coanda effect are obtained by the fitting algorithm. , , Based on the above gain circulation The calculation formula, and based on , , Specific rotational angular velocity and the velocity of the blowing jet To obtain a more accurate gain circulation The calculation formula is as follows: .

[0032] What needs to be known is the rotational angular velocity used in step four. Air jet velocity The value needs to iterate through all the angular velocities used in the second and third steps. Air jet velocity Ensure that the basic values ​​used are consistent, and ensure that the obtained gain circulation is consistent. The accuracy.

[0033] Specifically, , , The results can be obtained by fitting using the least squares method. The least squares method has the advantages of stable calculation, simple implementation, strong fitting of the overall trend, strong interpretability and clear physical meaning. It can quickly obtain calculation results, and the process is intuitive and the fitting effect is accurate.

[0034] Specifically, , , The solution process using the least squares method is as follows: Gain circumference Calculation formula Converted to And record , , And define the matrix: , , ; in, It is the flow control parameter matrix. It is the coupling gain circumductance matrix. It is a matrix of parameters to be determined; The relationship between the three matrices above is as follows: Then the undetermined parameter matrix is ​​estimated by least squares. The calculation formula is as follows: ; In this context, the superscript "-1" indicates the inverse of the correlation matrix, and the superscript "T" indicates the transpose of the correlation matrix. These are the nonlinear coupling gain fitting coefficients of the least squares fitting. , It is the fitting weight of rotational angular velocity and blowing jet velocity.

[0035] Specifically, the above matrix , and With three different sets of angular velocities and the velocity of the blowing jet For example, the three sets of angular velocities are respectively used This indicates the velocity of the three sets of air jets. To use separately express, , and Using three different sets of angular velocities and the velocity of the blowing jet It is expressed as follows: ; ; .

[0036] Specifically, the process of predicting lift in step six is ​​as follows: Total circulation The calculation formula is as follows: ; The formula for predicting lift is as follows: ; in, It is the incoming flow density. It is the incoming flow velocity; It is the total circulation volume; It predicts lift; Based on the specific cylindrical rotational angular velocity and blowing speed Substituting the above total circulation Γ 总 The calculation formula can be used to obtain the accurate predicted total circulation Γ of the current airfoil. 总 The total circulating volume Γ will be predicted. 总 Substitute into the predicted lift The calculation formula yields an accurate predicted lift for the airfoil under current flow conditions. .

[0037] Preferably, the above-mentioned increase in circulation In Increase circulation In and gain circulation In , , The least squares method is preferred for fitting, but Huber regression, ridge regression, Bayesian regression, and Gaussian regression algorithms can also be used. The specific fitting process will not be described in detail.

[0038] This invention also provides a readable storage medium on which a program or instruction is stored, and when the program or instruction is executed by a processor, it implements the steps of the method described above.

[0039] This invention also provides a diagnostic device, including a memory and a processor, wherein the memory stores a program, and the processor executes the program to implement the steps of the method described above.

[0040] This invention is described with reference to flowchart illustrations or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and block diagrams. Figure 1 One or two processes and / or a box Figure 1 A device that specifies the function in one or two boxes.

[0041] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or two processes and / or a box Figure 1 The function specified in one or two boxes.

[0042] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or two processes and / or a box Figure 1 The steps for the function specified in one or two boxes.

[0043] The above embodiments are merely preferred embodiments of the present invention and should not be construed as limiting the scope of protection of the present invention. Any non-substantial changes and substitutions made by those skilled in the art based on the present invention shall fall within the scope of protection claimed by the present invention.

Claims

1. A method for rapidly solving the circulation of an airfoil controlled by the Magnus and Coanda effects, characterized in that, include: Determine the circulation of the airfoil without control; The study investigates the increase in circulation when the rotating body at the airfoil generates the Magnus effect, and determines the increase in circulation using CFD. The study investigated the increase in circulation of the airfoil when the Coanda effect is generated by blowing air alone, and determined the increase in circulation using CFD. The gain circulation was studied when the rotating body at the airfoil tail fin rotated and air blowing was applied simultaneously, and the gain circulation was determined by CFD. The total circulation is determined by summing the circulation, the increase circulation, the increase circulation, and the gain circulation, and the predicted lift is obtained using the Zhukovsky lift formula.

2. The method according to claim 1, characterized in that, The specific process for determining the circulation of an airfoil without control is as follows: The lift is calculated by referring to the lift coefficient table and combining it with the incoming flow conditions, or by obtaining the lift through CFD, and the circulation is obtained according to the Zhukovsky lift formula. Alternatively, the circulation can be obtained directly through the Zhukovsky transformation combined with the Kutta condition.

3. The method according to claim 1, characterized in that, The process for determining the increase in circulation of a rotating body due to the Magnus effect is as follows: When the rotational speed of the rotating body at the airfoil tail is not high and the gas flow does not separate, the increase in circulation of the rotating body is linearly related to the angular velocity, and its linearity coefficient is the linearity coefficient of the Magnus effect. Using CFD, several sets of circulation values ​​are obtained for the rotating body rotating at different angular velocities. The circulation values ​​without control are subtracted from each of these values ​​to obtain the increase in circulation value corresponding to different angular velocities. Then, using multiple sets of angular velocities and the increase in circulation value, the linear fitting coefficients of the Magnus effect are obtained through a fitting algorithm. Finally, the increase in circulation value is derived based on the linear fitting coefficients of the Magnus effect and a specific angular velocity.

4. The method according to claim 3, characterized in that, The process for determining the increase in circulation of a rotating body due to the Coanda effect is as follows: When the velocity of the blowing jet is not high and the blowing jet develops along the rotating body without flow separation, the increase in circulation of the rotating body is linearly related to the jet velocity, and the linearity coefficient is the jet gain coefficient. Several sets of circulations at different blowing jet velocities are obtained using CFD. The circulations under no-control conditions are subtracted from each of these sets to obtain the increase in circulations corresponding to different blowing jet velocities. Using multiple sets of blowing jet velocities and increase in circulations, the jet gain fitting coefficients for the Coanda effect are obtained through a fitting algorithm. Based on the jet gain fitting coefficients and a specific blowing jet velocity, the increase in circulations are then derived.

5. The method according to claim 4, characterized in that, The process for determining the gain circulation of a rotating body due to the Magnus and Coanda effects is as follows: The gain circulation consists of the nonlinear coupling gain coefficient and the angular velocity. Power and jet velocity The product of powers is obtained by multiplying the powers, where... , These are the weights of the rotational angular velocity and the blowing jet velocity on the circulation of the coupling gain, respectively. The circulation of the rotating body at different rotational angular velocities and air jet velocities is obtained using CFD. The circulation under no-control conditions is then subtracted, followed by the increases in circulation due to the Magnus effect and the Coanda effect, yielding the gain circulation of the rotating body at different angular velocities and air jet velocities. The nonlinear coupling gain fitting coefficients and the angular velocity contribution fitting weights are then calculated using a fitting algorithm. Jet velocity contribution fitting weights Based on the nonlinear coupling gain fitting coefficients, , The gain circulation is derived from the specific blowing jet velocity and the rotational angular velocity of the rotating body.

6. The method according to claim 5, characterized in that, Nonlinear coupling gain fitting coefficients, angular velocity contribution fitting weights Jet velocity contribution fitting weights The solution can be obtained using the least squares method.

7. The method according to claim 4, characterized in that, The Magnus effect linear fitting coefficients and jet gain fitting coefficients were obtained by least squares fitting.

8. The method according to claim 4, characterized in that, The cross-sectional shape of the rotating body can be one of a circle, an ellipse, or a triangle.

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